Turner posted a message to Celtics fans on Instagram late Friday afternoon.
The deal cannot be officially signed until July 7, when a leaguewide moratorium on signings and trades is lifted.
During two seasons in Boston, Turner averaged 10 points, 5 rebounds and 5 assists over 27.8 minutes per game. Celtics coach Brad Stevens often leaned on Turner's ballhandling abilities, especially during the 2014-15 season. Turner started 57 games that season, often running the offense while rookie Marcus Smart got his feet wet.
Turner, 27, settled into a reserve role this past season (with Isaiah Thomas elevating to starting point guard) and finished fifth in NBA Sixth Man of the Year voting. Known for his ability to create off the dribble, especially pulling up from the midrange, Turner often poked fun at himself for shooting just 14.5 percent beyond the 3-point arc before the All-Star break. He then went out and shot 52.4 percent from long distance over the final two months of the season.
Before rejuvenating his career in Boston, the 6-foot-7 Turner was continually referenced as the No. 2 pick in the 2010 draft. With the Celtics, Turner embraced his supporting role and endeared himself to his coach and teammates with his personality. Turner also cemented his reputation as one of the most quotable players in the league.
Information from ESPN's Chris Forsberg was used in this report.